The invention relates to a process for the continuous production of a lower aliphatic alcohol having from 3 to 5 carbon atoms by the catalytic hydration of a lower aliphatic olefin with 3 to 5 carbon atoms in the presence of water and a strongly acidic cation exchange resin catalyst in a fixed bed reactor at a temperature of about 120.degree.-180.degree. C. and a pressure of about 40-200 bar, with removal of the product stream, separation of the alcohol from the product stream and recycling of the process water.